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8h
comment A fun card game involving probability, getting all 13 ranks (any suit(s)) vs. 5 in a row of red or black.
When cards are drawn without replacement, the number of states is much larger. That's the source of difficulty.
9h
comment A fun card game involving probability, getting all 13 ranks (any suit(s)) vs. 5 in a row of red or black.
Your last question seems amenable to analysis. Here the number of states is very reasonable, so the exact probability can be calculated, and perhaps there is even an analytic solution. If all you care about is approximation in the regime $n\to\infty$ (where $n$ is the size of the deck, say) then it is possible that with some effort good approximations can be given to the original problem, depending on the exact model.
10h
answered Let $f,g$ be continuous from $\mathbb R$ to $\mathbb R$
10h
answered Counting sequences using Catalan Numbers
10h
comment A fun card game involving probability, getting all 13 ranks (any suit(s)) vs. 5 in a row of red or black.
No, it probably cannot be done on paper. Even computing the exact probability seems hard, since a DFA would need to remember about $40$ bits of information, making it rather large (that's just for a single game!). One can come up with many different "fun games", so unless there is any other motivation, I don't see why one would bother to spend any more time on it, given that you can satisfy your curiosity using a computer simulation.
1d
comment Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
@RickyDemer Fortunately, these numbers are the only counterexamples.
1d
answered A result of Erdos: the multiplicative persistence of $n$ is at most $c\ln(\ln n)$
1d
revised Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
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1d
revised Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
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1d
comment Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
@Sameer Yes, I just realized that. But the same method would work.
1d
answered Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
1d
comment How can i prove using induction that the Hadamard matrices are orthogonal?
What do you mean "a property of the type of matrix"? It holds since it's actually true, but how do we know that? Since we can prove that.
1d
answered How can i prove using induction that the Hadamard matrices are orthogonal?
Apr
18
answered P vs NP and Countable vs Uncountable Decision Space
Apr
13
comment Why is Mergesort $O(n)$ rather than $O(n\log{n})$?
I used the standard version of the Master theorem. Take a look at the Wikipedia page on the Master theorem.
Apr
13
comment how to prove that the following is not a regular language?
You actually need $p-1$ to be larger than the pumping length, since otherwise $k$ could equal 1.
Apr
13
answered How to simplify expression with Fibonacci numbers
Apr
13
answered Trying to show that the set of all $2$-element subsets of a denumerable set is denumerable
Apr
13
answered infinite monkey problem - probability of an infinite sequence containing an infinite sequence
Apr
13
revised how to prove that the following is not a regular language?
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